Dataset Capstone

Overview

Part 3: Histograms and Hypothesis Testing

Preparing the Data

library(tidyverse)
library(plotly)
library(reshape2)

Attaching package: ‘reshape2’

The following object is masked from ‘package:tidyr’:

    smiths

exif <- read_csv("capstone_exif.csv")

Rows: 1116 Columns: 15── Column specification ────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (10): DateTimeOriginal, CreateDate, ModifyDate, Software, LensInfo, LensModel, ExposureTime, FocalLength, FocalLengthIn3...
dbl  (5): FlickrID, JFIFVersion, ISO, FNumber, BrightnessValue
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

img_data <- read_csv("capstone_img_data.csv")

Rows: 10955 Columns: 87── Column specification ────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (16): flickr, img_loc, the_image, crop_coords, center_rgb, post_top_hsl, post_2_hsl, post_3_hsl, post_4_hsl, post_5_hsl,...
dbl (70): using_id, img_width, img_height, do_img_at, sub_img, full_id, r_min, r_max, r_mean, r_mode, g_min, g_max, g_mean, ...
num  (1): vivid_count
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# after working with this data for 12 hours, I find out there are hidden characeters in my data that were not displaying in Excel.

imgsd_tidy$post_top_count <- as.integer(imgsd_tidy$post_top_count)
imgsd_tidy$post_2_count <- as.integer(imgsd_tidy$post_2_count)
imgsd_tidy$post_3_count <- as.integer(imgsd_tidy$post_3_count)
imgsd_tidy$post_4_count <- as.integer(imgsd_tidy$post_4_count)
imgsd_tidy$post_5_count <- as.integer(imgsd_tidy$post_5_count)
imgsd_tidy$post_6_count <- as.integer(imgsd_tidy$post_6_count)

imgsd_tidy$common_hsl_1_count <- as.integer(imgsd_tidy$common_hsl_1_count)
imgsd_tidy$common_hsl_2_count <- as.integer(imgsd_tidy$common_hsl_2_count)
imgsd_tidy$common_hsl_3_count <- as.integer(imgsd_tidy$common_hsl_3_count)
imgsd_tidy$common_hsl_4_count <- as.integer(imgsd_tidy$common_hsl_4_count)

imgsd_tidy$full_red_count <- as.integer(imgsd_tidy$full_red_count)
imgsd_tidy$full_orange_count <- as.integer(imgsd_tidy$full_orange_count)
imgsd_tidy$full_yellow_count <- as.integer(imgsd_tidy$full_yellow_count)
imgsd_tidy$full_green_count <- as.integer(imgsd_tidy$full_green_count)
imgsd_tidy$full_cyan_count <- as.integer(imgsd_tidy$full_cyan_count)
imgsd_tidy$full_blue_count <- as.integer(imgsd_tidy$full_blue_count)
imgsd_tidy$full_purple_count <- as.integer(imgsd_tidy$full_purple_count)
imgsd_tidy$full_mag_count <- as.integer(imgsd_tidy$full_mag_count)
imgsd_tidy$visib_red_count <- as.integer(imgsd_tidy$visib_red_count)
imgsd_tidy$visib_orange_count <- as.integer(imgsd_tidy$visib_orange_count)
imgsd_tidy$visib_yellow_count <- as.integer(imgsd_tidy$visib_yellow_count)
imgsd_tidy$visib_green_count <- as.integer(imgsd_tidy$visib_green_count)
imgsd_tidy$visib_cyan_count <- as.integer(imgsd_tidy$visib_cyan_count)
imgsd_tidy$visib_blue_count <- as.integer(imgsd_tidy$visib_blue_count)
imgsd_tidy$visib_purple_count <- as.integer(imgsd_tidy$visib_purple_count)
imgsd_tidy$visib_mag_count <- as.integer(imgsd_tidy$visib_mag_count)
imgsd_tidy$vivid_red_count <- as.integer(imgsd_tidy$vivid_red_count)
imgsd_tidy$vivid_orange_count <- as.integer(imgsd_tidy$vivid_orange_count)
imgsd_tidy$vivid_yellow_count <- as.integer(imgsd_tidy$vivid_yellow_count)
imgsd_tidy$vivid_green_count <- as.integer(imgsd_tidy$vivid_green_count)
imgsd_tidy$vivid_cyan_count <- as.integer(imgsd_tidy$vivid_cyan_count)
imgsd_tidy$vivid_blue_count <- as.integer(imgsd_tidy$vivid_blue_count)
imgsd_tidy$vivid_purple_count <- as.integer(imgsd_tidy$vivid_purple_count)
imgsd_tidy$vivid_mag_count <- as.integer(imgsd_tidy$vivid_mag_count)
imgsd_tidy$vivid_count <- as.integer(imgsd_tidy$vivid_count)

imgsd_tidy$gen_bright_count <- as.integer(imgsd_tidy$gen_bright_count)
imgsd_tidy$gen_dark_count <- as.integer(imgsd_tidy$gen_dark_count)

imgsd_tidy <- imgsd_tidy %>% mutate(total_pixels = full_red_count +
                                      full_orange_count +
                                      full_yellow_count +
                                      full_green_count +
                                      full_cyan_count +
                                      full_blue_count + 
                                      full_purple_count +
                                      full_mag_count)

# more type conversions
imgsd_tidy$total_pixels <- as.integer(imgsd_tidy$total_pixels)
imgsd_tidy$light_mean_val <- as.numeric(imgsd_tidy$light_mean_val)
imgsd_tidy$post_num_regions <- as.integer(imgsd_tidy$post_num_regions)
imgsd_tidy$r_mean <- as.numeric(imgsd_tidy$r_mean)
imgsd_tidy$g_mean <- as.numeric(imgsd_tidy$g_mean)
imgsd_tidy$b_mean <- as.numeric(imgsd_tidy$b_mean)


#establishing ratio columns
imgsd_ratio <- imgsd_tidy %>% 
  mutate(ratio_post_top_hsl = post_top_count / total_pixels) %>%
  mutate(ratio_post_2_hsl = post_2_count / total_pixels) %>%
  mutate(ratio_post_3_hsl = post_3_count / total_pixels) %>%
  mutate(ratio_post_4_hsl = post_4_count / total_pixels) %>%
  mutate(ratio_post_5_hsl = post_5_count / total_pixels) %>%
  mutate(ratio_post_6_hsl = post_6_count / total_pixels) %>%
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_full_oragne = full_orange_count / total_pixels) %>%
  mutate(ratio_full_yellow = full_yellow_count / total_pixels) %>%
  mutate(ratio_full_green = full_green_count / total_pixels) %>%  
  mutate(ratio_full_cyan = full_cyan_count / total_pixels) %>%  
  mutate(ratio_full_blue = full_blue_count / total_pixels) %>%  
  mutate(ratio_full_purple = full_purple_count / total_pixels) %>%  
  mutate(ratio_full_mag = full_mag_count / total_pixels) %>%  
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_visib_red = visib_red_count / total_pixels) %>%
  mutate(ratio_visib_oragne = visib_orange_count / total_pixels) %>%
  mutate(ratio_visib_yellow = visib_yellow_count / total_pixels) %>%
  mutate(ratio_visib_green = visib_green_count / total_pixels) %>%  
  mutate(ratio_visib_cyan = visib_cyan_count / total_pixels) %>%  
  mutate(ratio_visib_blue = visib_blue_count / total_pixels) %>%  
  mutate(ratio_visib_purple = visib_purple_count / total_pixels) %>%  
  mutate(ratio_visib_mag = visib_mag_count / total_pixels) %>%
  mutate(ratio_vivid_red = vivid_red_count / total_pixels) %>%
  mutate(ratio_vivid_oragne = vivid_orange_count / total_pixels) %>%
  mutate(ratio_vivid_yellow = vivid_yellow_count / total_pixels) %>%
  mutate(ratio_vivid_green = vivid_green_count / total_pixels) %>%  
  mutate(ratio_vivid_cyan = vivid_cyan_count / total_pixels) %>%  
  mutate(ratio_vivid_blue = vivid_blue_count / total_pixels) %>%  
  mutate(ratio_vivid_purple = vivid_purple_count / total_pixels) %>%  
  mutate(ratio_vivid_mag = vivid_mag_count / total_pixels) %>%
  mutate(ratio_vivid = vivid_count / total_pixels)

imgsd_tidy <- select(img_data, -c(flickr, img_loc, the_image, img_width, img_height, crop_coords, do_img_at, r_mode, b_mode, g_mode))

imgsd_tidy <- replace_na(imgsd_tidy, list(
  post_2_hsl = "(-1, -1, -1)",
  post_3_hsl = "(-1, -1, -1)",
  post_4_hsl = "(-1, -1, -1)",
  post_5_hsl = "(-1, -1, -1)",
  post_6_hsl = "(-1, -1, -1)"
  )
  )

exif_tidy <- exif_tidy %>% separate(create_date, into = c('full_date', 'time'), sep = " ", remove = TRUE) %>% separate(full_date, into = c('year', 'month', 'day'), sep = ":", remove = FALSE) 

exif_tidy$date <- as.Date(paste("1881", exif_tidy$month, exif_tidy$day, sep = "-"), format ="%Y-%m-%d")

subimg_qty <- imgsd_tidy %>% count(using_id)

good_ids <- subimg_qty[subimg_qty$n >=6, "using_id"]

imgsd_tidy <- imgsd_tidy %>% filter(using_id %in% good_ids$using_id)

exif_tidy <- exif_tidy %>% filter(flickr_id %in% good_ids$using_id)

# after working with this data for 12 hours, I find out there are hidden characeters in my data that were not displaying in Excel.

imgsd_tidy$post_top_count <- as.integer(imgsd_tidy$post_top_count)
imgsd_tidy$post_2_count <- as.integer(imgsd_tidy$post_2_count)
imgsd_tidy$post_3_count <- as.integer(imgsd_tidy$post_3_count)
imgsd_tidy$post_4_count <- as.integer(imgsd_tidy$post_4_count)
imgsd_tidy$post_5_count <- as.integer(imgsd_tidy$post_5_count)
imgsd_tidy$post_6_count <- as.integer(imgsd_tidy$post_6_count)

imgsd_tidy$common_hsl_1_count <- as.integer(imgsd_tidy$common_hsl_1_count)
imgsd_tidy$common_hsl_2_count <- as.integer(imgsd_tidy$common_hsl_2_count)
imgsd_tidy$common_hsl_3_count <- as.integer(imgsd_tidy$common_hsl_3_count)
imgsd_tidy$common_hsl_4_count <- as.integer(imgsd_tidy$common_hsl_4_count)

imgsd_tidy$full_red_count <- as.integer(imgsd_tidy$full_red_count)
imgsd_tidy$full_orange_count <- as.integer(imgsd_tidy$full_orange_count)
imgsd_tidy$full_yellow_count <- as.integer(imgsd_tidy$full_yellow_count)
imgsd_tidy$full_green_count <- as.integer(imgsd_tidy$full_green_count)
imgsd_tidy$full_cyan_count <- as.integer(imgsd_tidy$full_cyan_count)
imgsd_tidy$full_blue_count <- as.integer(imgsd_tidy$full_blue_count)
imgsd_tidy$full_purple_count <- as.integer(imgsd_tidy$full_purple_count)
imgsd_tidy$full_mag_count <- as.integer(imgsd_tidy$full_mag_count)
imgsd_tidy$visib_red_count <- as.integer(imgsd_tidy$visib_red_count)
imgsd_tidy$visib_orange_count <- as.integer(imgsd_tidy$visib_orange_count)
imgsd_tidy$visib_yellow_count <- as.integer(imgsd_tidy$visib_yellow_count)
imgsd_tidy$visib_green_count <- as.integer(imgsd_tidy$visib_green_count)
imgsd_tidy$visib_cyan_count <- as.integer(imgsd_tidy$visib_cyan_count)
imgsd_tidy$visib_blue_count <- as.integer(imgsd_tidy$visib_blue_count)
imgsd_tidy$visib_purple_count <- as.integer(imgsd_tidy$visib_purple_count)
imgsd_tidy$visib_mag_count <- as.integer(imgsd_tidy$visib_mag_count)
imgsd_tidy$vivid_red_count <- as.integer(imgsd_tidy$vivid_red_count)
imgsd_tidy$vivid_orange_count <- as.integer(imgsd_tidy$vivid_orange_count)
imgsd_tidy$vivid_yellow_count <- as.integer(imgsd_tidy$vivid_yellow_count)
imgsd_tidy$vivid_green_count <- as.integer(imgsd_tidy$vivid_green_count)
imgsd_tidy$vivid_cyan_count <- as.integer(imgsd_tidy$vivid_cyan_count)
imgsd_tidy$vivid_blue_count <- as.integer(imgsd_tidy$vivid_blue_count)
imgsd_tidy$vivid_purple_count <- as.integer(imgsd_tidy$vivid_purple_count)
imgsd_tidy$vivid_mag_count <- as.integer(imgsd_tidy$vivid_mag_count)
imgsd_tidy$vivid_count <- as.integer(imgsd_tidy$vivid_count)

imgsd_tidy$gen_bright_count <- as.integer(imgsd_tidy$gen_bright_count)
imgsd_tidy$gen_dark_count <- as.integer(imgsd_tidy$gen_dark_count)

imgsd_tidy <- imgsd_tidy %>% mutate(total_pixels = full_red_count +
                                      full_orange_count +
                                      full_yellow_count +
                                      full_green_count +
                                      full_cyan_count +
                                      full_blue_count + 
                                      full_purple_count +
                                      full_mag_count)

# more type conversions
imgsd_tidy$total_pixels <- as.integer(imgsd_tidy$total_pixels)
imgsd_tidy$light_mean_val <- as.numeric(imgsd_tidy$light_mean_val)
imgsd_tidy$post_num_regions <- as.integer(imgsd_tidy$post_num_regions)
imgsd_tidy$r_mean <- as.numeric(imgsd_tidy$r_mean)
imgsd_tidy$g_mean <- as.numeric(imgsd_tidy$g_mean)
imgsd_tidy$b_mean <- as.numeric(imgsd_tidy$b_mean)


#establishing ratio columns
imgsd_ratio <- imgsd_tidy %>% 
  mutate(ratio_post_top_hsl = post_top_count / total_pixels) %>%
  mutate(ratio_post_2_hsl = post_2_count / total_pixels) %>%
  mutate(ratio_post_3_hsl = post_3_count / total_pixels) %>%
  mutate(ratio_post_4_hsl = post_4_count / total_pixels) %>%
  mutate(ratio_post_5_hsl = post_5_count / total_pixels) %>%
  mutate(ratio_post_6_hsl = post_6_count / total_pixels) %>%
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_full_oragne = full_orange_count / total_pixels) %>%
  mutate(ratio_full_yellow = full_yellow_count / total_pixels) %>%
  mutate(ratio_full_green = full_green_count / total_pixels) %>%  
  mutate(ratio_full_cyan = full_cyan_count / total_pixels) %>%  
  mutate(ratio_full_blue = full_blue_count / total_pixels) %>%  
  mutate(ratio_full_purple = full_purple_count / total_pixels) %>%  
  mutate(ratio_full_mag = full_mag_count / total_pixels) %>%  
  mutate(ratio_full_red = full_red_count / total_pixels) %>%
  mutate(ratio_visib_red = visib_red_count / total_pixels) %>%
  mutate(ratio_visib_oragne = visib_orange_count / total_pixels) %>%
  mutate(ratio_visib_yellow = visib_yellow_count / total_pixels) %>%
  mutate(ratio_visib_green = visib_green_count / total_pixels) %>%  
  mutate(ratio_visib_cyan = visib_cyan_count / total_pixels) %>%  
  mutate(ratio_visib_blue = visib_blue_count / total_pixels) %>%  
  mutate(ratio_visib_purple = visib_purple_count / total_pixels) %>%  
  mutate(ratio_visib_mag = visib_mag_count / total_pixels) %>%
  mutate(ratio_vivid_red = vivid_red_count / total_pixels) %>%
  mutate(ratio_vivid_oragne = vivid_orange_count / total_pixels) %>%
  mutate(ratio_vivid_yellow = vivid_yellow_count / total_pixels) %>%
  mutate(ratio_vivid_green = vivid_green_count / total_pixels) %>%  
  mutate(ratio_vivid_cyan = vivid_cyan_count / total_pixels) %>%  
  mutate(ratio_vivid_blue = vivid_blue_count / total_pixels) %>%  
  mutate(ratio_vivid_purple = vivid_purple_count / total_pixels) %>%  
  mutate(ratio_vivid_mag = vivid_mag_count / total_pixels) %>%
  mutate(ratio_vivid = vivid_count / total_pixels)

Exploration

1D Histograms

• Vivid %

Due to a very large number of images that have fewer than 2% vivid pixels, Vivid Ratios are separated out into three segments: 0% vivid pixels, 0-1% vivid pixels, and more than 1% vivid pixels

vivid_ratio <- imgsd_ratio %>% select(ratio_vivid)
vivid_ratio$ratio_vivid <- as.numeric(vivid_ratio$ratio_vivid)

vivid_ratio <- vivid_ratio %>% mutate(
  ratio_rank = case_when(
    ratio_vivid == 0 ~ 0, 
    ratio_vivid > 0 & ratio_vivid < 0.01 ~ 1, 
    ratio_vivid >= 0.01 ~ 2)
  )

rr_counts <- count(vivid_ratio, ratio_rank)

vrr_pie <- plot_ly(rr_counts, labels=~factor(ratio_rank), values= ~n, type='pie')

vrr_pie

# 0 -> No Vivid Pixels
# 1 -> 0-1% vivid pixels
# 2 -> more than 1% vivid pixels

Less vivid pixels than expected! Way less! Only 359 images/subimages had more than 1% of pixels with more than 70% saturation and lightness between 40 and 70%

Now let’s get back to seeing the distribution of those 359 values:

vivid_hist <- vivid_ratio %>% filter(ratio_rank == 2)

fig <- plot_ly(vivid_hist,
               x= ~ratio_vivid,
               type = "histogram")

fig

Future investigation will perform these calculations on the main dataframe in order to access specific image IDs and evaluate the subjective qualities of the top vivid images.

• Post-num (filter by img segment)

Investigating the distribution of how many posterization “clumps” were in each image

#first setting up filters for more useful faceting going forward
r_fig_filter_0 <- imgsd_ratio %>% filter(imgsd_ratio$sub_img == 0)
r_fig_filter_a <- imgsd_ratio[imgsd_ratio$sub_img %in% c(1, 2, 3), ]
r_fig_filter_b <- imgsd_ratio[imgsd_ratio$sub_img %in% c(4, 5, 6), ]
r_fig_filter_c <- imgsd_ratio[imgsd_ratio$sub_img %in% c(7, 8, 9), ]


fig_0 <- ggplot(r_fig_filter_0,
               aes(x=post_num_regions)) + 
                geom_histogram(binwidth = 5)

fig_a <- ggplot(r_fig_filter_a,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_b <- ggplot(r_fig_filter_b,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_c <- ggplot(r_fig_filter_c,
              aes(x=post_num_regions)) + 
              geom_histogram(binwidth = 5) +
              facet_grid (~ sub_img)

fig_0b <- ggplot(r_fig_filter_0,
               aes(x=post_num_regions)) + 
                geom_histogram(binwidth = 50)

fig_0

fig_0b

fig_a

fig_b

fig_c

No huge conclusions to draw about the distribution in sub_image 0, other than the x-scale is shown as roughly 10x (slightly less) than the subimages. Also mildly interesting (also on sub_img 0), the max count for any given bin (at bin-width 5), is a fraction of the scale of the other sub_images. Bumping the sub_img 0 binwidth up to 50 (10x), brings it more in line with the counts in the sub_images, but the long tail on sub_img 0 keeps it from matching exactly.

Otherwise, the only noteworthy observation is the less-intense right skew on sub_images 2, 5, and 8.

These sub-images represent the horizontal middle third of their source images, mimicking the artistic principles of the rule of thirds and putting focal points near the center of the image.

• Exif brightness

EXIF data, I have not forsaken you.

fig <- ggplot(exif_tidy,
               aes(x=brightness_value)) + 
                geom_histogram(bins=250)

fig

That’s the most normal distribution we’ve seen yet! But still pretty irregular. Let’s see how it compares to the HSL data

• Mean_lightness

fig_all <- ggplot(imgsd_ratio,
               aes(x=light_mean_val)) + 
                geom_histogram(bins=250)

fig_0 <- ggplot(r_fig_filter_0,
               aes(x=light_mean_val)) + 
                geom_histogram(bins=250)

fig_a <- ggplot(r_fig_filter_a,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)

fig_b <- ggplot(r_fig_filter_b,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)

fig_c <- ggplot(r_fig_filter_c,
              aes(x=light_mean_val)) + 
              geom_histogram(bins=250) +
              facet_grid(~ sub_img)


fig_all

fig_0

fig_a

fig_b

fig_c

Observations: Variation among sub-images is fairly minor, with some some possibility that corner quadrants (1, 3, 7, 9) have wider distributions overall. Lightness values processed for this dataset are centered around 0.625 with a slight left skew. While the EXIF data has a less-normal distribution, it does seem to have a center slightly to the right of its baseline value, but the irregularity of the shape looks more like a right skew than left.

• (r/g/b) mean
  

fig <- plot_ly(imgsd_ratio, alpha = .4)
fig <- fig %>% add_histogram(x = ~r_mean)
fig <- fig %>% add_histogram(x = ~g_mean)
fig <- fig %>% add_histogram(x = ~b_mean)
fig <- fig %>% layout(barmode = 'overlay', colorway=c('red', 'green', 'blue'))

fig

Observation: No special information here. As expected, it looks a lot like the mean lightness value distrbution. Almost as if r+g+b = light….

• Date distribution (with and without year)

fig <- plot_ly(exif_tidy, x = ~date, type = 'histogram')

fig_all <- plot_ly(exif_tidy, x = ~full_date, type = 'histogram')

fig

fig_all

Observation: Even when adjusting for year, the distribution of images is highly irregular. As a month, August is over-represented, and as an individual date, Will and Taylor’s wedding is over-represented.

exif_tidy$time <- strptime(exif_tidy$time, format = "%H:%M%S")

fig <- plot_ly(exif_tidy, x = ~time, type = 'histogram')
fig

Error: C stack usage  15924272 is too close to the limit

Analysis

Final data prep!

Slimming down the EXIF data frame….

#slimming down exif columns....

simple_exif <- exif_tidy %>% select(c(flickr_id, date, month, time, software, jfifversion, brightness_value))

… and adding those EXIF columns to the main dataframe

simple_exif <- simple_exif %>%
  mutate(flickr_id = as.character(flickr_id))

# bringing it all full circle with this variable choice

all_img_data <- imgsd_ratio %>% 
  left_join(simple_exif, by = c("using_id" = "flickr_id"))

Warning: Detected an unexpected many-to-many relationship between `x` and `y`.

#this throws a warning about many-to-many relationships, but this is expected behavior

This space reserved for re-creating sub-frames for ‘faceting’

At last, let’s revisit those hypotheses

H1 - Hue vs Date

\(Ho:\) There is no correlation between time of year and color values

\(Ha:\) Warm color values are more prominent between May and September

Gut Check - Due to the uneven distribution of sample images over time, I don’t have a strong expectation of valid results.

exif_tidy$month <- as.integer(exif_tidy$month)

season_split <- exif_tidy %>% mutate(
  season = case_when(
    month >= 5 & month <= 9 ~ 1, TRUE ~ 0)
  )

season_counts <- table(season_split$season)
season_data <- data.frame(ratio = names(season_counts), count = as.vector(season_counts))

season_data

On the other hand, summer values (622) don’t outrageously outnumber non-summer values.

Now to collect the hue information we will be comparing

all_img_data <- all_img_data %>% 
  mutate(visib_warm = visib_red_count + visib_orange_count + visib_yellow_count + visib_mag_count) %>%
  mutate(visib_cool = visib_green_count + visib_cyan_count + visib_blue_count + visib_purple_count)
  
h1_frame <- all_img_data %>% 
  select(c(using_id, sub_img, total_pixels, visib_warm, visib_cool, date, month)) %>% 
  mutate(warm_ratio = visib_warm / total_pixels) %>% 
  mutate(cool_ratio = visib_cool/total_pixels) %>% 
  mutate(season = case_when(month >= 5 & month <= 9 ~ 1, TRUE ~ 0)) %>%
  mutate(ratio_diff = warm_ratio - cool_ratio)

Testing Time

t.test(warm_ratio ~ season, h1_frame)

    Welch Two Sample t-test

data:  warm_ratio by season
t = 11.179, df = 9078.6, p-value < 2.2e-16
alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
95 percent confidence interval:
 0.01619583 0.02308347
sample estimates:
mean in group 0 mean in group 1 
     0.04115762      0.02151798 

Conclusion

Despite my hesitation, the results of the T-test are strongly in favor of rejecting the null hypothesis that there is no difference in visible warmth throughout the year. A high t-value and low p-value are both in support of this conclusion.

Post Script:

Additional Hypotheses:

H2 - Lightness vs Time

\(Ho:\) There is no correlation between time of day and lightness values

\(Ha:\) Lightness values are higher between 6 am and 6pm

H3 - Saturation vs Subject

\(Ho:\) There is no correlation between saturation and being a picture of my cat

\(Ha:\) Low saturation values are increasingly common over time, especially in central sub-images

H4 - Vividness vs Image Type

\(Ho:\) Vivid ratio (percentage of vivid pixels) is uniformly distributed among all Software types

\(Ha:\) Vivid ratio is consistently highest in Slow Shutter Cam photos without JFIF values